what is the name of the prime number pattern for primes listed in a sequence?

Question

There's a principle that states that most prime numbers in a linear sequence will occur in groups, separated by only one number, i.e 5 and 7, 11 and 13, 17 and 19, 29, 31 and 33. Does anyone know the name of that principle?

Answer 1

this is a twin prime...
twin prime is a prime number that differs from another prime number by two. Except for the pair (2, 3), this is the smallest possible difference between two primes. Some examples of twin prime pairs are 5 and 7, 11 and 13, and 821 and 823. (Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin.)

examples
(3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73), (101, 103), (107, 109), (137, 139), (149, 151), (179, 181), (191, 193), (197, 199), (227, 229), (239, 241), (269, 271), (281, 283), (311, 313), (347, 349), (419, 421), (431, 433), (461, 463), (521, 523), (569, 571), (599, 601), (617, 619), (641, 643), (659, 661), (809, 811), (821, 823), (827, 829), (857, 859), (881, 883)

Answer 2

There is a new way of studying simple mathematical problems in a graphical way. Copying Eratosthenes we introduce a sieve in the form of layers of prime multiples represented as binary bands. Those layers have a totally determined frequency and they are fully symmetric. By means of this method we will see that the position of prime numbers is far away from being random, on the contrary, it has a totally determined structure, at least not directly. Finally we will see that some unsolved problems like Goldbach conjecture and related ones, are based in hidden symmetries to be proved. Look at the source below for full report which may answer your question.

Answer 3

Optimus Prime

Answer 4

There's something called the Twin Prime Conjecture.